Simplify to lowest terms. $\dfrac{81}{45}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 81 and 45? $81 = 3\cdot3\cdot3\cdot3$ $45 = 3\cdot3\cdot5$ $\mbox{GCD}(81, 45) = 3\cdot3 = 9$ $\dfrac{81}{45} = \dfrac{9 \cdot 9}{ 5\cdot 9}$ $\hphantom{\dfrac{81}{45}} = \dfrac{9}{5} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{81}{45}} = \dfrac{9}{5} \cdot 1$ $\hphantom{\dfrac{81}{45}} = \dfrac{9}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{81}{45}= \dfrac{3\cdot27}{3\cdot15}= \dfrac{3\cdot 3\cdot9}{3\cdot 3\cdot5}= \dfrac{9}{5}$